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A167783
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Numbers that are repdigits with length > 2 in more than one base.
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1
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0, 31, 63, 255, 273, 364, 511, 546, 728, 777, 931, 1023, 1365, 1464, 2730, 3280, 3549, 3783, 3906, 4095, 4557, 6560, 7566, 7812, 8191, 9114, 9331, 9841, 10507, 11349, 11718, 13671, 14043, 14763, 15132, 15624, 16383, 18291, 18662, 18915, 19608
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OFFSET
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1,2
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COMMENTS
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Definition requires "length > 2" because all numbers, n > 2, are trivially represented as "11" in base n-1.
0 included at the suggestion of Franklin T. Adams-Watters (and others) as 0 = 000 in any base.
Contribution from Daniel Forgues, Nov 13 2009: (Start)
0 = 00 = 000 = 0000 = 00000 = 000000 = 0000000 = 00000000 = ... in any positional number representation (includes fixed base radix b > 1, mixed base radix with each b_i > 1, i >= 0, such as factorial and primorial based radix...)
The sequence definition should be read as:
Nonnegative integers that are repdigits with length > 2 in more than one fixed base radix b > 1.
Considering all fixed and mixed base radix would include many more nonnegative integers (but not the integers 1 to 6) which are repdigits with length > 2 in more than one radix. (End)
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LINKS
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Table of n, a(n) for n=1..41.
Wolfram Demonstrations Project, Mixed Radix Number Representations [From Daniel Forgues, Nov 13 2009]
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EXAMPLE
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31 is in the list because 31 (base 10) = 11111 (base 2) = 111 (base 5)
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CROSSREFS
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Cf. A167782 - Numbers that are repdigits with length > 2 in some base
Cf. A010785 - Repdigits (base 10)
Cf. A053696 - Numbers which are repunits in some base
Cf. A158235 - Numbers n whose square can be represented as a repdigit number in some base < n
Sequence in context: A042910 A042908 A042912 * A042914 A042916 A042918
Adjacent sequences: A167780 A167781 A167782 * A167784 A167785 A167786
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KEYWORD
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nonn,base
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AUTHOR
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Andrew Weimholt, Nov 12 2009
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STATUS
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approved
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